Hinge Theorem

Front

What does the Hinge Theorem state?

Back

The Hinge Theorem states that if two triangles have two sides of one triangle congruent to two sides of another triangle, and the included angles are not equal, then the triangle with the larger included angle has a longer third side.

Front

How can you express the relationship between angles using symbols?

Back

You can express the relationship between angles using symbols such as '>' for greater than, '<' for less than, and '=' for equal.

Front

If m∠BAC > m∠EDF, what can be inferred about the lengths of the sides opposite these angles?

Back

If m∠BAC > m∠EDF, then the side opposite m∠BAC is longer than the side opposite m∠EDF.

Front

What is the significance of comparing angles in triangles?

Back

Comparing angles in triangles helps determine the relative lengths of the sides opposite those angles, which is crucial for solving problems involving triangle properties.

Front

What is the relationship between the angles and sides in a triangle according to the Hinge Theorem?

Back

According to the Hinge Theorem, the larger the included angle between two sides, the longer the side opposite that angle.

Front

How do you denote the measure of an angle?

Back

The measure of an angle is denoted using 'm∠' followed by the angle's name, for example, m∠ABC.

Front

What can be concluded if m∠EAC < m∠FBD?

Back

If m∠EAC < m∠FBD, then the side opposite m∠EAC is shorter than the side opposite m∠FBD.

Front

What is the importance of the Hinge Theorem in solving triangle problems?

Back

The Hinge Theorem is important in solving triangle problems as it allows for the comparison of side lengths based on the measures of the included angles.

Front

What does it mean if two angles are congruent?

Back

If two angles are congruent, it means they have the same measure.

Front

How can you compare two segments using the Hinge Theorem?

Back

You can compare two segments by analyzing the angles formed by the segments and applying the Hinge Theorem to determine which segment is longer.